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1Zero dissipation limit to a Riemann solution consisting of two shock waves for the 1D compressible isentropic Navier-Stokes equations显示文摘We investigate the zero dissipation limit problem of the one-dimensional compressible isentropic Navier-Stokes equations with Riemann initial data in the case of the composite wave of two shock waves.It is shown that the unique solution to the Navier-Stokes equations exists for all time,and converges to the Riemann solution to the corresponding Euler equations with the same Riemann initial data uniformly on the set away from the shocks,as the viscosity vanishes.In contrast to previous related works,where either the composite wave is absent or the efects of initial layers are ignored,this gives the frst mathematical justifcation of this limit for the compressible isentropic Navier-Stokes equations in the presence of both composite wave and initial layers.Our method of proof consists of a scaling argument,the construction of the approximate solution and delicate energy estimates.ZHANG YingHui PAN RongHua TAN Zhong panrh@math.gatech.edu, ztan85@163.com 2013Science China Mathematics2013,56,11:6
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